The second-order Cornish-Fisher cumulant expansion permits
to approximatively redress the normal quantiles by taking into account the skewness and the "taildeness" of
a non-normal distribution [1]}, [2]}. The observed RV is statistically significant at level \(\alpha \)  if (one-tailed test)
\(\begin{split}&\qquad \qquad \qquad \underbrace{\frac{{\tt RV}- \mathbb {E}({\tt RV})}{\sqrt{\mbox{$\mathbb {V}$ar}({\tt RV})}}}_{\mbox{\small \em $z$-score}} \qquad \: \: > \: \: \underbrace{u_{1-\alpha }}_{\mbox{\small \em standard normal quantile}} \qquad \\& +\quad \underbrace{\frac{\mbox{$\mathbb {A}$}({\tt RV})}{6}(u^2_{1-\alpha }-1)+\frac{{\mathchoice{\raisebox {}{\scalebox {1}[-1]{\displaystyle \mathbb {L}}}}{\raisebox {}{\scalebox {1}[-1]{\textstyle \mathbb {L}}}}{\raisebox {}{\scalebox {1}[-1]{\scriptstyle \mathbb {L}}}}{\raisebox {}{\scalebox {1}[-1]{\scriptscriptstyle \mathbb {L}}}}}({\tt RV})}{24}(u^3_{1-\alpha }-3u_{1-\alpha })-\frac{\mbox{$\mathbb {A}^2$}({\tt RV})}{36}(2u^3_{1-\alpha }-5u_{1-\alpha })}_{\mbox{\small \em correction to the normal distribution}}\hspace{5.0pt}.\end{split}\) 
